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Mastering Trigonometric Ratios in Right-Angled Triangles

Delve into the world of trigonometry with a focus on sine and cosine ratios in right-angled triangles. Learn to identify and define hypotenuse, opposite, and adjacent sides, explore the relationships between angles and trigonometric values, and practice calculating sin, cos, and tan ratios for various angles. Understand the practical applications of these concepts to describe triangle properties and relationships effectively.

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Mastering Trigonometric Ratios in Right-Angled Triangles

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  1. The sine and cosine ratios Explicit teaching

  2. The sine and cosine ratios – part 1 Visible learning Learning intentions  To be able to use language associated with trigonometry to describe features, properties and relationships within right-angled triangles.  To know and be able to define the trigonometric ratios of sine, cosine and tangent. Success criteria  I can identify the hypotenuse, opposite and adjacent sides with respect to a given angle in a right-angled triangle.  I can explain the relationship between the value of sin30 found in my calculator and a right-angled triangle with a 30?angle.  I can write three trigonometric ratios for a given angle in a right-angled triangle.

  3. Trigonometric ratios – part 1 Hypotenuse 3

  4. Trigonometric ratios – part 2 Opposite 4

  5. Trigonometric ratios – part 3 Adjacent 5

  6. Trigonometric ratios – part 4 Summarise sin36.9?=3 What do you notice? 5 cos36.9?=4 5 tan36.9?=3 4 What do you wonder? sin53.1?=4 5 cos53.1?=3 5 tan53.1?=4 3 6

  7. Success criteria  I can identify the hypotenuse, opposite and adjacent sides with respect to a given angle in a right-angled triangle.  I can explain the relationship between the value of sin30° found in my calculator and a right-angled triangle with a 30?angle.  I can write three trigonometric ratios for a given angle in a right-angled triangle.

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